Sum of the radius of the base and height of a cylinder is 21 cm and the curved surface area of the cylinder is 616 sq. cm, find the total surface area of the cylinder.

925.04cm²

Step-by-step explanation:

Curved surface area of a cylinder = 2πrh

r is the radius

h is the height

If the sum of the radius of the base and height of the cylinder is 21 cm, then;

r + h = 21

r = 21-h 1

Recall:

CSA =  2πrh

616 = 2πrh 2

Substitute equation 1 into 2;

616 = 2π(21-h)h

616 = 2π(21h-h²)

616 = 42(3.14)h - 2(3.14)h²

616 = 131.88h - 6.28h²

98.09 = 21h - h²

h²-21h+98.09 = 0

h = 21±√21²-4(98.09)/2

h = 21±√441-392.36/2

h = 21±√48.64/2

h = 21±6/97/2

h = 21+6.97/2 and 21-6.97/2

h = 27.97/2 and 14.03/2

h = 13.985 and 7.015

Since r = 21-h

r = 21 - 13.985

Using r = 7.015

The total surface area = 2πrh + 2πr²

The total surface area = 616 + 2(3.14)7.015²

The total surface area = 616 + 309.04

The total surface area = 925.04

Hence the total surface area of the cylinder is 925.04cm²

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above